This paper intends to conform the mathematical correspondence between electric and mechanical variables to the physical correspondence in electroelastic problem when a piezoelectric material is subjected to stress field
\sigma_{ij}
and electric field
E_i
or displacement
{\bf u}
and electric displacement
D_i
.
E_i
is expressed with an antisymmetric electric field tensor
V_{ij}
, and
D_i
is expressed with an antisymmetric electric displacement tensor
P_{ij}
which can be expressed with ‘induction potential’
\psi_i
. Then stress equilibrium and electric field equations can be described by a second order canonical differential equation system of
u_i
and
\psi_i
. As an example, the coupled electroelastic fields in an inclusion or inhomogeneity embedded in an infinite matrix are obtained in a manner directly analogous to Eshelby’s classical elastic solution. The electroelastic fields inside the ellipsoidal inclusion or inhomogeneity and just outside the ellipsoidal inclusion or inhomogeneity are also given. In addition, we analyze the energies of the inclusion. The results in this paper are the backbone in the development of the electric damage theory and ferroelectric constitutive theory.
